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Casimir energy for the interaction of -plates with a massless real scalar field.

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Title: Casimir energy for the interaction of -plates with a massless real scalar field.
Authors: Kraskov, M. V.1 (AUTHOR) misakraskov@mail.ru, Pis'mak, Yu. M.1 (AUTHOR) y.pismak@spbu.ru
Source: Theoretical & Mathematical Physics. Jun2026, Vol. 227 Issue 3, p1026-1037. 12p.
Subjects: Scalar field theory, Functional integration, Potential theory (Mathematics), Matrices (Mathematics), Vacuum energy (Astronomy), Boundary value problems, Chebyshev polynomials
Abstract: Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of planar -plates with an interaction potential. Using functional integration and the Sylvester identity, the interaction energy density (per unit area) can be reduced to the logarithm of the determinant of an matrix. After subtracting the self-energy contribution, the geometry of the system allows the problem to be reduced to calculating the determinant of a tridiagonal matrix, which is evaluated using a recurrence relation. For a system of identical plates with equal separations, we obtain a closed expression in terms of Chebyshev polynomials. As an illustration of the efficiency of the method, an explicit form for is written out, and the limiting case of infinitely strong interaction (), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates and the separation , at fixed thickness and with weak coupling constant , the system of -films approaches a finite-thickness slab. The results are verified for the particular cases and. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Within the Symanzik approach, we consider a massless real scalar field in Euclidean spacetime in the presence of planar -plates with an interaction potential. Using functional integration and the Sylvester identity, the interaction energy density (per unit area) can be reduced to the logarithm of the determinant of an matrix. After subtracting the self-energy contribution, the geometry of the system allows the problem to be reduced to calculating the determinant of a tridiagonal matrix, which is evaluated using a recurrence relation. For a system of identical plates with equal separations, we obtain a closed expression in terms of Chebyshev polynomials. As an illustration of the efficiency of the method, an explicit form for is written out, and the limiting case of infinitely strong interaction (), which is associated with Dirichlet boundary conditions, is considered. In addition, we show that in the case where the number of plates and the separation , at fixed thickness and with weak coupling constant , the system of -films approaches a finite-thickness slab. The results are verified for the particular cases and. [ABSTRACT FROM AUTHOR]
ISSN:00405779
DOI:10.1134/S0040577926060097